The Projection Iteration For Inverse Problems

By using discrete regularization theories,the general nonstationary iteration,which was utilized to solve the(finite-dimensional)singular linear equations,was promoted and a type of projection iteration was obtained,which can be used to solve the ill-posed operator equations of the first kind.Under the situations of precise data and disturbed data,we provided the convergence conditions of this projection iteration respectively(including the proof of the convergence)as well as the stopping rule and the choice of parameters.As corollaries,the quotient convergence of the projection iteration scheme and the equivalent semi-norm convergence were given.As the application,we also discussed how to solve a concrete integral equation by using the projection iteration,including the proper method to discrete L2 space,the choice of generating operators,stopping rule,the choice of parameters,and the corresponding error analysis.